Right-angled polyhedra and hyperbolic 3-manifolds Full article
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Russian Mathematical Surveys
ISSN: 0036-0279 , E-ISSN: 1468-4829 |
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| Output data | Year: 2017, Volume: 72, Number: 2, Pages: 335-374 Pages count : 40 DOI: 10.1070/RM9762 | ||
| Tags | Colourings of polyhedra; Hamiltonian graphs; Hyperbolic 3-manifolds; Right-angled reflection groups; Small covers; Volumes of manifolds | ||
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Abstract:
Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. © 2017 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.
Cite:
Vesnin A.Y.
Right-angled polyhedra and hyperbolic 3-manifolds
Russian Mathematical Surveys. 2017. V.72. N2. P.335-374. DOI: 10.1070/RM9762 WOS Scopus OpenAlex
Right-angled polyhedra and hyperbolic 3-manifolds
Russian Mathematical Surveys. 2017. V.72. N2. P.335-374. DOI: 10.1070/RM9762 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000406101400003 |
| Scopus: | 2-s2.0-85026679620 |
| OpenAlex: | W2616482100 |